Bound the UMFPACK-backed sparse cachevals to the eltypes UMFPACK has

[ChrisRackauckas-Claude]

Please ignore until reviewed by @ChrisRackauckas.

Found while checking what the sparse default does per element type. Reproduces on a pristine checkout of main.

The bug

A = sparse(Float32(1)I, 50, 50) + spdiagm(1=>fill(0.1f0,49)); b = ones(Float32, 50)
LinearSolve.defaultalg(A, b, OperatorAssumptions(true))
# => DefaultLinearSolver(DefaultAlgorithmChoice.KLUFactorization, true, false)
init(LinearProblem(A,b), nothing)
# => MethodError: no method matching SparseArrays.UMFPACK.UmfpackLU(::SparseMatrixCSC{Float32, Int64})

The algorithm that throws is not the one selected. _init_default_cacheval (src/default.jl, @generated) emits an unconditional init_cacheval for every slot — only the three Krylov slots are guarded — so a too-permissive init_cacheval on an unselected algorithm still breaks init. KLU is chosen; the LUFactorization slot is constructed first and throws.

LUFactorization's and UMFPACKFactorization's sparse cachevals are bounded by BLASELTYPES = Union{Float32,Float64,ComplexF32,ComplexF64}, but UmfpackLU exists only for Float64/ComplexF64 (SuiteSparse's UMFVTypes) — too wide by exactly Float32/ComplexF32. KLU already gets this right with T <: KLU.KLUTypes.

4 of 10 eltype/index combinations fail on unmodified main:

Int64/Float32     INIT THREW    Int32/Float32     INIT THREW
Int64/ComplexF32  INIT THREW    Int32/ComplexF32  INIT THREW

The fix

Bound them to a local UMFPACKELTYPES = Union{Float64, ComplexF64}.

Two notes on the shape of it:

• The extra BLASELTYPES method is not redundant. The old methods' is_cusparse(A) → cudss_loaded(A) ? lu_instance(A) : nothing branch is the only LUFactorization+CuSparse init_cacheval in the tree (LinearSolveCUDAExt defines none), so narrowing alone would have silently dropped Float32 cuDSS support.
• UMFPACKELTYPES is defined locally rather than reusing SparseArrays.UMFPACK.UMFVTypes, which is a non-public internal.

Float32/ComplexF32 sparse now resolve to the KLUFactorization slot, which algchoice_to_alg maps to PureKLUFactorization() — pure Julia, a hard dependency, and the only thing in the tree that actually supports these eltypes (SuiteSparse KLU, UMFPACK, and Sparspak all reject them).

Bisect — two separate breakages

commit	date	effect
0ce03c28	2025-05-22	widened the cachevals to T <: BLASELTYPES while adding ComplexF64. Broke Float32 sparse for Sparspak users; everyone else still hit the "using Sparspak required" error in defaultalg first, so it stayed hidden.
52ebf258 (#1037)	2026-06-13	removed that early error, exposing the breakage to everyone.

Measured at 0ce03c28^ with Sparspak loaded: init OK. So this path did work once.

Testing

All 10 combinations after the fix — eltype preserved, no silent Float64 promotion:

Float32/Int64     OK resid=0.0  eltype=Float32
ComplexF32/Int32  OK resid=0.0  eltype=ComplexF32
BigFloat/Int64    OK resid=1.7e-77

• test/Core/default_algs.jl gains a 4-combination testset (Float32/ComplexF32 × Int64/Int32). Confirmed it executes: Default Alg Tests goes 89 → 109 tests.
• GROUP=Core passes on the fixed tree and on unmodified main — main is not independently red.
• Test.detect_ambiguities on the extension: 12 before, 12 after.
• Runic reports no formatting changes.

Out of scope

Explicitly-requested LUFactorization/UMFPACKFactorization on Float32 sparse remain unsupported, exactly as before this change — they now fail the way SuiteSparse KLU already does for an unsupported eltype instead of with a MethodError. Making them work would mean silent Float32→Float64 promotion (SparseArrays' lu does this), which is a behavior addition rather than a bug fix. Happy to do it separately if you want it.

Also cleared while looking: BigFloat sparse is not a second bug — the KLUFactorization enum slot maps to PureKLUFactorization, not SuiteSparse KLU, so it works today. And Symmetric Float32 sparse → CHOLMOD is fine, because CHOLMOD's init_cacheval returns nothing for the non-Float64 case.

🤖 Generated with Claude Code

https://claude.ai/code/session_017rr42T1vFRRT8D7DMAmJzf